Majority-vote model on proximity graphs with variable disorder

Complex network theory has substantial application in human group emergent behavior due to its ability to represent and analyze the interconnected nature of social systems. Its applications range from sociology to network science, providing valuable knowledge for various fields of study and real-world scenarios. We study the effects of Gabriel Graphs proximity interactions on opinion dynamics. Our network assumes the Euclidean distribution of nodes to form a square lattice, and we consider a σ parameter that displaces the coordinates of the nodes randomly. We analyze network effects on the majority-vote opinion dynamics with social temperature q that drives dissensus. Using Monte Carlo simulations, we obtain magnetization, susceptibility, and Binder cumulant for different values of σ displacement. Our results show that the system undergoes a second-order phase transition that depends on lattice disorder and social temperature.